Analytic families of reducible linear quasi-periodic differential equations

• DOI: 10.1017/s0143385705000362
• Publication Date: 2006-03-17T10:44:06Z
• Authors: JOAQUIM PUIG; CARLES SIMÓ
• Keywords: Constant coefficients; Forcing (mathematics); Matrix (chemical analysis); Constant (computer programming); Quasi periodic

In this paper we study the existence of analytic families reducible linear quasi-periodic differential equations in matrix Lie algebras. Under suitable conditions show, by means a Kolmogorov–Arnold–Moser (KAM) scheme, that real system close to constant can be modified addition time-free makes it coefficients. If depends analytically on external parameters, then modifying term is also analytic.As major application, prove analyticity resonance tongue boundaries Hill's equation with small forcing. Several consequences for spectrum Schrödinger operators forcing are derived. particular, that, generically, and potential has all spectral gaps open and, therefore, Cantor set. Some other applications included systems .